The one-dimensional quantum Ising model is one of the most studied quantum systems. In a transeverse field, it possesses a quantum critical point. For non-critical transverse field it can be described by free massive Majorana fermions. With critical transverse field, in the presence of finite longitudinal field it can be described by the $E_8$ integrable model. I will present our studies on the time evolution of entanglement entropy after a global (mass) quench in both cases, comparing scaling field theory results to exact and numerical spin chain calculations extrapolated to the scaling limit. I will discuss the linear in time growth of entanglement and its suppression, and long living entanglement oscillations.

The talk is based on the recent works:
O. A. Castro-Alvaredo, M. Lencsés, I. M. Szécsényi, J. Viti: Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach, JHEP 1912 (2019) 079, JHEP 2019 (2020) 079, arXiv:1907.11735
O. A. Castro-Alvaredo, M. Lencsés, I. M. Szécsényi, J. Viti: Entanglement Oscillations near a Quantum Critical Point, arXiv:2001.10007